In many applications of adaptive control it may be clear if the unknown parameters are constants or are time varying functions. It may be especially difficult to determine if some of the parameters are constants or slowly varying functions of time. To determine parameter variations it is necessary to "forget" the past of the state. The approach of exponential discounting of past information has...

We consider the following cake cutting game: Alice chooses a set P of n points in the square (cake) [0, 1], where (0, 0) ∈ P ; Bob cuts out n axis-parallel rectangles with disjoint interiors, each of them having a point of P as the lower left corner; Alice keeps the rest. It has been conjectured that Bob can always secure at least half of the cake. This remains unsettled, and it is not even kno...

The list Ramsey number R ℓ ( H , k ) ${R}_{\ell }(H,k)$ recently introduced by Alon, Bucić, Kalvari, Kuperwasser, and Szabó, is a list-coloring variant of the classical number. They showed that if $H$ fixed r $r$ -uniform hypergraph not -partite colors $k$ goes to infinity, e Ω ≤ O ${e}^{{\rm{\Omega }}(\sqrt{k})}\le {R}_{\ell }(H,k)\le {e}^{O(k)}$ . We prove = Θ }(H,k)={e}^{{\rm{\Theta }}(k)}$ ...